Assessing Avocado Pricing Dynamics Utilizing Climate, Transportation Cost, and Macroeconomic Metrics in California¶

Problem Statement:¶

In recent years, avocados have seen a surge in popularity across social media platforms, leading to an exponential increase in demand and establishing them as one of the most popular fruits globally. Research by Mordor Intelligence (Avocado Market Insights, n.d.) forecasts substantial growth in the avocado market, with the projected market size expected to rise from USD 22.69 billion in 2024 to USD 35.55 billion by 2029. Additionally, the USDA reports annual per capita consumption of avocados exceeding 8 pounds in the North American market, with local production and imports serving as the primary sources of supply (Avocado Market Insights, n.d.).

Given the perishable nature of avocados, maintaining fruit quality heavily depends on a robust supply chain that efficiently manages harvesting, transportation, and distribution processes. As avocado demand continues to escalate, understanding the driving factors behind market expansion becomes imperative.

This project focuses on California, a leading region in both avocado cultivation and consumption, with the specific aim of identifying primary drivers influencing avocado price fluctuations within the state. By analyzing critical components of the avocado supply chain—production, transportation, and consumer behavior—the objective is to develop a robust regression model that not only forecasts future avocado prices but also highlights the importance of each factor influencing these prices. The goal is to achieve a comprehensive understanding of avocado pricing dynamics by incorporating features representing various stages of the supply chain.

Steps:¶

  1. Data Collection:

    • Production Data: Collect climatic data from key production regions (Uruapan, Michoacan, Mexico, and Fallbrook, California) from Weather of the World, covering temperature, precipitation, humidity, wind speed, atmospheric pressure, and other relevant factors.
    • Transportation Cost Data: Gather energy consumption expenses, including unit prices of electricity, petroleum, and natural gas in California from the U.S. Energy Information Administration (EIA).
    • Consumer and Economic Data: Obtain economic variables such as the Consumer Price Index, Personal Consumption Expenditures, Producer Price Index, Inflation Rate, and Unemployment Rate from the Federal Reserve Economic Data (FRED).
    • Target Variable: Collect weekly avocado price data for California from the Kaggle dataset "Avocado Prices and Sales Volume 2015-2023."

  2. Data Examination:

    • Identify and handle missing values and outliers within the dataset.
    • Aggregate data to monthly data points and compute monthly averages for model development.
    • Review correlations between different attributes to understand interdependencies and refine feature selection for model development.

  3. Data Description:

    • Provide detailed descriptions of the collected data for each component: Avocado Price Data, Plantation Data (Uruapan and Fallbrook), California Energy Data, and Economic Data.

  4. Exploratory Data Analysis (EDA):

    • KDE Plots: Create KDE plots for each attribute to visualize their distributions.
    • Correlation Analysis: Generate correlation heatmaps to identify relationships between attributes.
    • Pairwise Distribution: Plot pairwise distributions of attributes to examine their interactions.

  5. Model Development:

    • Feature Engineering: Select and engineer relevant features based on EDA findings.
    • Regression Model: Develop a regression model to forecast avocado prices, incorporating features representing various stages of the supply chain.

  6. Model Evaluation:

    • Evaluate the model's performance using appropriate metrics such as RMSE, MAE, and R-squared.
    • Interpret the model to understand the importance of each factor influencing avocado prices.

  7. Conclusion:

    • Summarize findings and insights derived from the model.
    • Discuss the implications of these findings for avocado pricing dynamics and potential applications in supply chain management.

  8. Report Writing:

    • Compile the findings, methodologies, and conclusions into a comprehensive project report.
    • Include visualizations, data descriptions, and model interpretations to support the analysis.

By following these steps, the project aims to provide a detailed understanding of the factors driving avocado price fluctuations in California, ultimately aiding in better forecasting and supply chain management strategies.

Part I - EDA¶

In [1]:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib import rcParams
import seaborn as sns
import warnings
from IPython.core.interactiveshell import InteractiveShell
from statsmodels.tsa.stattools import adfuller
In [2]:
# Setting configurations

# Ignore warnings to avoid cluttering the output
warnings.filterwarnings('ignore')

# Set the plot style to 'ggplot' for aesthetic consistency
plt.style.use('ggplot')

# Configure matplotlib parameters to remove right and top spines, and set figure size
rcParams['axes.spines.right'] = False
rcParams['axes.spines.top'] = False
rcParams['figure.figsize'] = [12, 9]

# Set font size for plot labels and titles
rcParams['font.size'] = 16

# Set tick label sizes for both x and y axes
plt.rc('xtick', labelsize=12)
plt.rc('ytick', labelsize=12)

# Set custom color palette for seaborn plots
sns.set_palette(['#74a09e', '#86c1b2', '#98e2c6',
                '#f3c969', '#f2a553', '#d96548', '#c14953'])

# Configure inline figure format for high-resolution displays
%config InlineBackend.figure_format = 'retina'

# Disable Jedi for auto-completion to potentially improve performance in large notebooks
%config Completer.use_jedi = False

# Set maximum column width for pandas DataFrame display
pd.set_option('max_colwidth', 40)

# Display all columns of pandas DataFrames without truncation
pd.options.display.max_columns = None

# Allow all expressions to produce multiple outputs in IPython shell
InteractiveShell.ast_node_interactivity = 'all'

# Set random seed for reproducibility in random number generation
np.random.seed(42)
In [3]:
# Loading Data
input_data = pd.read_excel('Data_project.xls')
input_data.head()
Out[3]:
Year_Month Year Month Is_Organic Unemployment_Level Unemployment_Level_Lead2 Unemployment_Rate Unemployment_Rate_Lead2 Median_Consumer_Price_Index Median_Consumer_Price_Index_Lead2 Personal_Consumption_Expenditures Personal_Consumption_Expenditures_Lead2 Number_Unemployed_for_27_Weeks_&_over Number_Unemployed_for_27_Weeks_&_over_Lead2 Average_Hourly_Earnings_of_All_Employees Average_Hourly_Earnings_of_All_Employees_Lead2 Federal_Funds_Effective_Rate Federal_Funds_Effective_Rate_Lead2 Employed_Persons_in_California Employed_Persons_in_California_Lead2 Labor_Force_Participation_Rate_for_California Labor_Force_Participation_Rate_for_California_Lead2 California_Gas_Price California_NG_Price California_Electricity_Price Temperature_Uruapan Sea_Level_Pressure_Uruapan Humidity_Uruapan Wind_Speed_Uruapan Visibility_Uruapan Dew_point_temperature_Uruapan Temperature_Fallbrook Sea_Level_Pressure_Fallbrook Humidity_Fallbrook Wind_Speed_Fallbrook Visibility_Fallbrook Dew_point_temperature_Fallbrook Avocado_Volume Avocado_Price
0 201501 2015 1 0 8885 9090 5.7 5.8 1.947530 2.256311 12066.7 12083.9 2774 2828 24.75 24.66 0.11 0.09 17513360 17451977 62.3 62.4 2.596 9.436667 14.55 19.061947 635.875221 65.601770 2.000000 17.190400 11.823009 14.600514 745.208895 54.552699 1.538817 14.875681 3.757841 5.575767e+06 0.9825
1 201501 2015 1 1 8885 9090 5.7 5.8 1.947530 2.256311 12066.7 12083.9 2774 2828 24.75 24.66 0.11 0.09 17513360 17451977 62.3 62.4 2.596 9.436667 14.55 19.061947 635.875221 65.601770 2.000000 17.190400 11.823009 14.600514 745.208895 54.552699 1.538817 14.875681 3.757841 1.543415e+05 1.2200
2 201502 2015 2 0 8599 8717 5.5 5.6 1.954495 2.383394 12116.6 12096.1 2658 2799 24.79 24.62 0.11 0.12 17539526 17484592 62.3 62.4 2.756 8.960000 14.30 17.801887 635.096226 69.198113 1.320755 19.773585 11.424528 15.616625 743.596898 61.901985 1.638337 14.462779 6.569479 6.638805e+06 0.9200
3 201502 2015 2 1 8599 8717 5.5 5.6 1.954495 2.383394 12116.6 12096.1 2658 2799 24.79 24.62 0.11 0.12 17539526 17484592 62.3 62.4 2.756 8.960000 14.30 17.801887 635.096226 69.198113 1.320755 19.773585 11.424528 15.616625 743.596898 61.901985 1.638337 14.462779 6.569479 1.454359e+05 1.3475
4 201503 2015 3 0 8515 8885 5.4 5.7 2.433336 1.947530 12176.1 12066.7 2542 2774 24.86 24.75 0.11 0.11 17566611 17513360 62.3 62.3 3.388 8.960000 14.22 19.078431 635.006000 68.745098 2.385621 15.735948 12.333333 17.691583 743.619033 56.874372 1.791457 14.905528 6.533291 5.832235e+06 1.0040
In [4]:
input_data.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 216 entries, 0 to 215
Data columns (total 39 columns):
 #   Column                                               Non-Null Count  Dtype  
---  ------                                               --------------  -----  
 0   Year_Month                                           216 non-null    int64  
 1   Year                                                 216 non-null    int64  
 2   Month                                                216 non-null    int64  
 3   Is_Organic                                           216 non-null    int64  
 4   Unemployment_Level                                   216 non-null    int64  
 5   Unemployment_Level_Lead2                             216 non-null    int64  
 6   Unemployment_Rate                                    216 non-null    float64
 7   Unemployment_Rate_Lead2                              216 non-null    float64
 8   Median_Consumer_Price_Index                          216 non-null    float64
 9   Median_Consumer_Price_Index_Lead2                    216 non-null    float64
 10  Personal_Consumption_Expenditures                    216 non-null    float64
 11  Personal_Consumption_Expenditures_Lead2              216 non-null    float64
 12  Number_Unemployed_for_27_Weeks_&_over                216 non-null    int64  
 13  Number_Unemployed_for_27_Weeks_&_over_Lead2          216 non-null    int64  
 14  Average_Hourly_Earnings_of_All_Employees             216 non-null    float64
 15  Average_Hourly_Earnings_of_All_Employees_Lead2       216 non-null    float64
 16  Federal_Funds_Effective_Rate                         216 non-null    float64
 17  Federal_Funds_Effective_Rate_Lead2                   216 non-null    float64
 18  Employed_Persons_in_California                       216 non-null    int64  
 19  Employed_Persons_in_California_Lead2                 216 non-null    int64  
 20  Labor_Force_Participation_Rate_for_California        216 non-null    float64
 21  Labor_Force_Participation_Rate_for_California_Lead2  216 non-null    float64
 22  California_Gas_Price                                 216 non-null    float64
 23  California_NG_Price                                  216 non-null    float64
 24  California_Electricity_Price                         216 non-null    float64
 25  Temperature_Uruapan                                  216 non-null    float64
 26  Sea_Level_Pressure_Uruapan                           216 non-null    float64
 27  Humidity_Uruapan                                     216 non-null    float64
 28  Wind_Speed_Uruapan                                   216 non-null    float64
 29  Visibility_Uruapan                                   216 non-null    float64
 30  Dew_point_temperature_Uruapan                        216 non-null    float64
 31  Temperature_Fallbrook                                216 non-null    float64
 32  Sea_Level_Pressure_Fallbrook                         216 non-null    float64
 33  Humidity_Fallbrook                                   216 non-null    float64
 34  Wind_Speed_Fallbrook                                 216 non-null    float64
 35  Visibility_Fallbrook                                 216 non-null    float64
 36  Dew_point_temperature_Fallbrook                      216 non-null    float64
 37  Avocado_Volume                                       216 non-null    float64
 38  Avocado_Price                                        216 non-null    float64
dtypes: float64(29), int64(10)
memory usage: 65.9 KB
In [5]:
input_data.isnull().sum()
Out[5]:
Year_Month                                             0
Year                                                   0
Month                                                  0
Is_Organic                                             0
Unemployment_Level                                     0
Unemployment_Level_Lead2                               0
Unemployment_Rate                                      0
Unemployment_Rate_Lead2                                0
Median_Consumer_Price_Index                            0
Median_Consumer_Price_Index_Lead2                      0
Personal_Consumption_Expenditures                      0
Personal_Consumption_Expenditures_Lead2                0
Number_Unemployed_for_27_Weeks_&_over                  0
Number_Unemployed_for_27_Weeks_&_over_Lead2            0
Average_Hourly_Earnings_of_All_Employees               0
Average_Hourly_Earnings_of_All_Employees_Lead2         0
Federal_Funds_Effective_Rate                           0
Federal_Funds_Effective_Rate_Lead2                     0
Employed_Persons_in_California                         0
Employed_Persons_in_California_Lead2                   0
Labor_Force_Participation_Rate_for_California          0
Labor_Force_Participation_Rate_for_California_Lead2    0
California_Gas_Price                                   0
California_NG_Price                                    0
California_Electricity_Price                           0
Temperature_Uruapan                                    0
Sea_Level_Pressure_Uruapan                             0
Humidity_Uruapan                                       0
Wind_Speed_Uruapan                                     0
Visibility_Uruapan                                     0
Dew_point_temperature_Uruapan                          0
Temperature_Fallbrook                                  0
Sea_Level_Pressure_Fallbrook                           0
Humidity_Fallbrook                                     0
Wind_Speed_Fallbrook                                   0
Visibility_Fallbrook                                   0
Dew_point_temperature_Fallbrook                        0
Avocado_Volume                                         0
Avocado_Price                                          0
dtype: int64
In [6]:
input_data['Is_Organic'].value_counts()
Out[6]:
Is_Organic
0    108
1    108
Name: count, dtype: int64
In [7]:
print(f"total numbers of Months: {len(input_data['Year_Month'].unique())}")
input_data['Year_Month'].unique()

total numbers of Months: 108
Out[7]:
array([201501, 201502, 201503, 201504, 201505, 201506, 201507, 201508,
       201509, 201510, 201511, 201512, 201601, 201602, 201603, 201604,
       201605, 201606, 201607, 201608, 201609, 201610, 201611, 201612,
       201701, 201702, 201703, 201704, 201705, 201706, 201707, 201708,
       201709, 201710, 201711, 201712, 201801, 201802, 201803, 201804,
       201805, 201806, 201807, 201808, 201809, 201810, 201811, 201812,
       201901, 201902, 201903, 201904, 201905, 201906, 201907, 201908,
       201909, 201910, 201911, 201912, 202001, 202002, 202003, 202004,
       202005, 202006, 202007, 202008, 202009, 202010, 202011, 202012,
       202101, 202102, 202103, 202104, 202105, 202106, 202107, 202108,
       202109, 202110, 202111, 202112, 202201, 202202, 202203, 202204,
       202205, 202206, 202207, 202208, 202209, 202210, 202211, 202212,
       202301, 202302, 202303, 202304, 202305, 202306, 202307, 202308,
       202309, 202310, 202311, 202312])
In [8]:
input_data.columns
Out[8]:
Index(['Year_Month', 'Year', 'Month', 'Is_Organic', 'Unemployment_Level',
       'Unemployment_Level_Lead2', 'Unemployment_Rate',
       'Unemployment_Rate_Lead2', 'Median_Consumer_Price_Index',
       'Median_Consumer_Price_Index_Lead2',
       'Personal_Consumption_Expenditures',
       'Personal_Consumption_Expenditures_Lead2',
       'Number_Unemployed_for_27_Weeks_&_over',
       'Number_Unemployed_for_27_Weeks_&_over_Lead2',
       'Average_Hourly_Earnings_of_All_Employees',
       'Average_Hourly_Earnings_of_All_Employees_Lead2',
       'Federal_Funds_Effective_Rate', 'Federal_Funds_Effective_Rate_Lead2',
       'Employed_Persons_in_California',
       'Employed_Persons_in_California_Lead2',
       'Labor_Force_Participation_Rate_for_California',
       'Labor_Force_Participation_Rate_for_California_Lead2',
       'California_Gas_Price', 'California_NG_Price',
       'California_Electricity_Price', 'Temperature_Uruapan',
       'Sea_Level_Pressure_Uruapan', 'Humidity_Uruapan', 'Wind_Speed_Uruapan',
       'Visibility_Uruapan', 'Dew_point_temperature_Uruapan',
       'Temperature_Fallbrook', 'Sea_Level_Pressure_Fallbrook',
       'Humidity_Fallbrook', 'Wind_Speed_Fallbrook', 'Visibility_Fallbrook',
       'Dew_point_temperature_Fallbrook', 'Avocado_Volume', 'Avocado_Price'],
      dtype='object')
In [9]:
# Column Groups
avocado_col = ['Year', 'Month', 'Is_Organic',
               'Avocado_Volume', 'Avocado_Price']
eco_cols = [
    'Unemployment_Level', 'Unemployment_Rate', 'Median_Consumer_Price_Index',
    'Personal_Consumption_Expenditures', 'Number_Unemployed_for_27_Weeks_&_over',
    'Average_Hourly_Earnings_of_All_Employees', 'Federal_Funds_Effective_Rate',
    'Employed_Persons_in_California', 'Labor_Force_Participation_Rate_for_California'
]
eco_lead2_cols = [
    'Unemployment_Level_Lead2', 'Unemployment_Rate_Lead2', 'Median_Consumer_Price_Index_Lead2',
    'Personal_Consumption_Expenditures_Lead2', 'Number_Unemployed_for_27_Weeks_&_over_Lead2',
    'Average_Hourly_Earnings_of_All_Employees_Lead2', 'Federal_Funds_Effective_Rate_Lead2',
    'Employed_Persons_in_California_Lead2', 'Labor_Force_Participation_Rate_for_California_Lead2'
]
weather_fallbrook = [
    'Temperature_Fallbrook', 'Sea_Level_Pressure_Fallbrook', 'Humidity_Fallbrook',
    'Wind_Speed_Fallbrook', 'Visibility_Fallbrook', 'Dew_point_temperature_Fallbrook'
]
weather_uruapan = [
    'Temperature_Uruapan', 'Sea_Level_Pressure_Uruapan', 'Humidity_Uruapan',
    'Wind_Speed_Uruapan', 'Visibility_Uruapan', 'Dew_point_temperature_Uruapan'
]
ca_energy = ['California_Gas_Price',
             'California_NG_Price', 'California_Electricity_Price']

Avocado Price Data¶

In [10]:
# Descriptive Statistics for Avocado Data
with pd.option_context('float_format', '{:f}'.format):
    input_data[avocado_col].describe().T
Out[10]:
count mean std min 25% 50% 75% max
Year 216.000000 2019.000000 2.587987 2015.000000 2017.000000 2019.000000 2021.000000 2023.000000
Month 216.000000 6.500000 3.460071 1.000000 3.750000 6.500000 9.250000 12.000000
Is_Organic 216.000000 0.500000 0.501161 0.000000 0.000000 0.500000 1.000000 1.000000
Avocado_Volume 216.000000 3036990.358403 2852572.101494 82368.292500 222202.941875 2169131.171000 5841954.779500 7653057.877500
Avocado_Price 216.000000 1.509203 0.355675 0.825000 1.223255 1.481788 1.790987 2.325000
In [11]:
# Preparing Avocado Price Data
input_data_price = input_data[['Year_Month',
                               'Is_Organic', 'Avocado_Price']].copy()
input_data_price['Type'] = np.where(
    input_data_price['Is_Organic'] == 0, 'Conventional', 'Organic')
input_data_price['date_column'] = pd.to_datetime(
    input_data_price['Year_Month'], format='%Y%m')
In [12]:
# Plotting Avocado Prices Over Time
plt.figure(figsize=(20, 5))
sns.lineplot(
    x='date_column', y='Avocado_Price', data=input_data_price, hue='Type',
    marker='o', palette={'Organic': 'forestgreen', 'Conventional': 'darkseagreen'},
    hue_order=['Organic', 'Conventional']
)
plt.title('\nAvocado Price Overtime: Organic & Conventional\n', fontsize=13)
plt.xlabel('Year_Month', fontsize=12)
plt.ylabel('Price', fontsize=12)
plt.legend(title='Type', fontsize=10)
plt.show()
Out[12]:
<Figure size 2000x500 with 0 Axes>
Out[12]:
<Axes: xlabel='date_column', ylabel='Avocado_Price'>
Out[12]:
Text(0.5, 1.0, '\nAvocado Price Overtime: Organic & Conventional\n')
Out[12]:
Text(0.5, 0, 'Year_Month')
Out[12]:
Text(0, 0.5, 'Price')
Out[12]:
<matplotlib.legend.Legend at 0x7af1bbc6ead0>
No description has been provided for this image
In [13]:
# ADF Test
result = adfuller(input_data_price['Avocado_Price'])
print('ADF Statistic:', result[0])
print('p-value:', result[1])

ADF Statistic: -3.0788845531376032
p-value: 0.028155805053984274

Economic Data¶

In [14]:
# Descriptive Statistics for Economic Data
with pd.option_context('float_format', '{:f}'.format):
    input_data[eco_cols].describe().T
Out[14]:
count mean std min 25% 50% 75% max
Unemployment_Level 216.000000 7666.101852 2812.828794 5698.000000 6070.000000 6753.500000 7968.750000 23090.000000
Unemployment_Rate 216.000000 4.752778 1.808068 3.400000 3.700000 4.200000 5.025000 14.800000
Median_Consumer_Price_Index 216.000000 3.436477 1.710645 1.092895 2.293325 2.897937 4.134864 8.048036
Personal_Consumption_Expenditures 216.000000 14777.619444 2070.833871 12066.700000 13127.025000 14201.500000 16452.625000 19013.700000
Number_Unemployed_for_27_Weeks_&_over 216.000000 1828.305556 808.172057 965.000000 1262.250000 1553.500000 2127.000000 4174.000000
Average_Hourly_Earnings_of_All_Employees 216.000000 28.668981 2.887263 24.750000 26.155000 27.985000 31.000000 34.340000
Federal_Funds_Effective_Rate 216.000000 1.409167 1.572856 0.050000 0.120000 0.845000 2.145000 5.330000
Employed_Persons_in_California 216.000000 18030973.333333 602621.626383 15643297.000000 17752987.000000 18286905.500000 18419367.500000 18732265.000000
Labor_Force_Participation_Rate_for_California 216.000000 61.912037 0.665945 59.600000 61.800000 62.100000 62.300000 63.000000
In [15]:
# Correlation Heatmap for Economic Data
plt.figure(figsize=(10, 8))
sns.heatmap(input_data[eco_cols].corr(), annot=True,
            cmap='Blues', fmt='.2f', linewidths=0.5)
plt.title('\nCorrelation Heatmap of Economic Factors\n', fontsize=14)
plt.show()
Out[15]:
<Figure size 1000x800 with 0 Axes>
Out[15]:
<Axes: >
Out[15]:
Text(0.5, 1.0, '\nCorrelation Heatmap of Economic Factors\n')
No description has been provided for this image
In [16]:
# KDE Plots for Economic Data
eco_cols_new = [
    'Unemployment_Rate', 'Median_Consumer_Price_Index', 'Personal_Consumption_Expenditures',
    'Number_Unemployed_for_27_Weeks_&_over', 'Federal_Funds_Effective_Rate',
    'Labor_Force_Participation_Rate_for_California'
]
In [17]:
fig, axes = plt.subplots(2, 3, figsize=(20, 10))
for i, col in enumerate(eco_cols_new):
    row, col_idx = divmod(i, 3)
    sns.kdeplot(data=input_data, x=col,
                ax=axes[row, col_idx], color='cornflowerblue', fill=True)
    sns.rugplot(input_data[col], ax=axes[row, col_idx],
                color='royalblue', linewidth=1, height=0.04)
    axes[row, col_idx].set_title(f'KDE of {col}', fontsize=10)
    axes[row, col_idx].tick_params(axis='both', which='major', labelsize=10)
    axes[row, col_idx].set_xlabel(col, fontsize=10)
    axes[row, col_idx].set_ylabel('Density', fontsize=10)
plt.subplots_adjust(hspace=0.4, wspace=0.4)
plt.show()
Out[17]:
<Axes: xlabel='Unemployment_Rate', ylabel='Density'>
Out[17]:
<Axes: xlabel='Unemployment_Rate', ylabel='Density'>
Out[17]:
Text(0.5, 1.0, 'KDE of Unemployment_Rate')
Out[17]:
Text(0.5, 0, 'Unemployment_Rate')
Out[17]:
Text(0, 0.5, 'Density')
Out[17]:
<Axes: xlabel='Median_Consumer_Price_Index', ylabel='Density'>
Out[17]:
<Axes: xlabel='Median_Consumer_Price_Index', ylabel='Density'>
Out[17]:
Text(0.5, 1.0, 'KDE of Median_Consumer_Price_Index')
Out[17]:
Text(0.5, 0, 'Median_Consumer_Price_Index')
Out[17]:
Text(0, 0.5, 'Density')
Out[17]:
<Axes: xlabel='Personal_Consumption_Expenditures', ylabel='Density'>
Out[17]:
<Axes: xlabel='Personal_Consumption_Expenditures', ylabel='Density'>
Out[17]:
Text(0.5, 1.0, 'KDE of Personal_Consumption_Expenditures')
Out[17]:
Text(0.5, 0, 'Personal_Consumption_Expenditures')
Out[17]:
Text(0, 0.5, 'Density')
Out[17]:
<Axes: xlabel='Number_Unemployed_for_27_Weeks_&_over', ylabel='Density'>
Out[17]:
<Axes: xlabel='Number_Unemployed_for_27_Weeks_&_over', ylabel='Density'>
Out[17]:
Text(0.5, 1.0, 'KDE of Number_Unemployed_for_27_Weeks_&_over')
Out[17]:
Text(0.5, 0, 'Number_Unemployed_for_27_Weeks_&_over')
Out[17]:
Text(0, 0.5, 'Density')
Out[17]:
<Axes: xlabel='Federal_Funds_Effective_Rate', ylabel='Density'>
Out[17]:
<Axes: xlabel='Federal_Funds_Effective_Rate', ylabel='Density'>
Out[17]:
Text(0.5, 1.0, 'KDE of Federal_Funds_Effective_Rate')
Out[17]:
Text(0.5, 0, 'Federal_Funds_Effective_Rate')
Out[17]:
Text(0, 0.5, 'Density')
Out[17]:
<Axes: xlabel='Labor_Force_Participation_Rate_for_California', ylabel='Density'>
Out[17]:
<Axes: xlabel='Labor_Force_Participation_Rate_for_California', ylabel='Density'>
Out[17]:
Text(0.5, 1.0, 'KDE of Labor_Force_Participation_Rate_for_California')
Out[17]:
Text(0.5, 0, 'Labor_Force_Participation_Rate_for_California')
Out[17]:
Text(0, 0.5, 'Density')
No description has been provided for this image
In [18]:
# Pairplot for Economic Data
pairplot = sns.pairplot(input_data[eco_cols_new], plot_kws={
                        'color': 'cornflowerblue'}, diag_kws={'color': 'cornflowerblue'})
pairplot.fig.suptitle(
    '\nPairwise Distribution of Economic Factors\n\n', fontsize=13, y=1.06)
pairplot.fig.set_size_inches(20, 18)
# Adjust the font size of the leftmost y-axis labels
for i, ax in enumerate(pairplot.axes[:, 0]):
    ax.set_ylabel(ax.get_ylabel(), fontsize=8)

# Adjust the font size of the bottom x-axis labels
for ax in pairplot.axes[-1, :]:
    ax.set_xlabel(ax.get_xlabel(), fontsize=8)
plt.show()
Out[18]:
Text(0.5, 1.06, '\nPairwise Distribution of Economic Factors\n\n')
Out[18]:
Text(51.9861111111111, 0.5, 'Unemployment_Rate')
Out[18]:
Text(78.3611111111111, 0.5, 'Median_Consumer_Price_Index')
Out[18]:
Text(36.2361111111111, 0.5, 'Personal_Consumption_Expenditures')
Out[18]:
Text(46.8611111111111, 0.5, 'Number_Unemployed_for_27_Weeks_&_over')
Out[18]:
Text(78.3611111111111, 0.5, 'Federal_Funds_Effective_Rate')
Out[18]:
Text(67.8611111111111, 0.5, 'Labor_Force_Participation_Rate_for_California')
Out[18]:
Text(0.5, 52.11111111111096, 'Unemployment_Rate')
Out[18]:
Text(0.5, 52.11111111111096, 'Median_Consumer_Price_Index')
Out[18]:
Text(0.5, 52.11111111111096, 'Personal_Consumption_Expenditures')
Out[18]:
Text(0.5, 52.11111111111096, 'Number_Unemployed_for_27_Weeks_&_over')
Out[18]:
Text(0.5, 52.11111111111096, 'Federal_Funds_Effective_Rate')
Out[18]:
Text(0.5, 52.11111111111096, 'Labor_Force_Participation_Rate_for_California')
No description has been provided for this image

Fallbrook weather data¶

In [19]:
# Descriptive Statistics for Fallbrook Weather Data
with pd.option_context('float_format', '{:f}'.format):
    input_data[weather_fallbrook].describe().T
Out[19]:
count mean std min 25% 50% 75% max
Temperature_Fallbrook 216.000000 17.055303 3.596314 9.760880 14.216468 16.461810 20.562465 23.619718
Sea_Level_Pressure_Fallbrook 216.000000 742.658457 1.427656 740.314450 741.386022 742.240842 743.934006 745.576340
Humidity_Fallbrook 216.000000 66.793920 10.396502 31.916667 61.128533 69.056502 74.600565 85.405244
Wind_Speed_Fallbrook 216.000000 1.857397 0.312388 1.186298 1.617894 1.809621 2.091785 2.660128
Visibility_Fallbrook 216.000000 14.792203 0.627279 13.053333 14.414525 14.882023 15.236255 15.897059
Dew_point_temperature_Fallbrook 216.000000 9.192613 5.230041 -4.534498 4.933694 8.579012 13.898736 16.815232
In [20]:
# Correlation Heatmap for Fallbrook Weather Data
plt.figure(figsize=(10, 8))
sns.heatmap(input_data[weather_fallbrook].corr(),
            annot=True, cmap='Greens', fmt='.2f', linewidths=0.5)
plt.title('\nCorrelation Heatmap of Fallbrook Weather Factors\n', fontsize=14)
plt.show()
Out[20]:
<Figure size 1000x800 with 0 Axes>
Out[20]:
<Axes: >
Out[20]:
Text(0.5, 1.0, '\nCorrelation Heatmap of Fallbrook Weather Factors\n')
No description has been provided for this image
In [21]:
# KDE Plots for Fallbrook Weather Data
fig, axes = plt.subplots(2, 3, figsize=(20, 10))
for i, col in enumerate(weather_fallbrook):
    row, col_idx = divmod(i, 3)
    sns.kdeplot(data=input_data, x=col,
                ax=axes[row, col_idx], color='forestgreen', fill=True)
    sns.rugplot(input_data[col], ax=axes[row, col_idx],
                color='seagreen', linewidth=1, height=0.04)
    axes[row, col_idx].set_title(f'KDE of {col}', fontsize=10)
    axes[row, col_idx].tick_params(axis='both', which='major', labelsize=10)
    axes[row, col_idx].set_xlabel(col, fontsize=10)
    axes[row, col_idx].set_ylabel('Density', fontsize=10)
plt.subplots_adjust(hspace=0.4, wspace=0.4)
plt.show()
Out[21]:
<Axes: xlabel='Temperature_Fallbrook', ylabel='Density'>
Out[21]:
<Axes: xlabel='Temperature_Fallbrook', ylabel='Density'>
Out[21]:
Text(0.5, 1.0, 'KDE of Temperature_Fallbrook')
Out[21]:
Text(0.5, 0, 'Temperature_Fallbrook')
Out[21]:
Text(0, 0.5, 'Density')
Out[21]:
<Axes: xlabel='Sea_Level_Pressure_Fallbrook', ylabel='Density'>
Out[21]:
<Axes: xlabel='Sea_Level_Pressure_Fallbrook', ylabel='Density'>
Out[21]:
Text(0.5, 1.0, 'KDE of Sea_Level_Pressure_Fallbrook')
Out[21]:
Text(0.5, 0, 'Sea_Level_Pressure_Fallbrook')
Out[21]:
Text(0, 0.5, 'Density')
Out[21]:
<Axes: xlabel='Humidity_Fallbrook', ylabel='Density'>
Out[21]:
<Axes: xlabel='Humidity_Fallbrook', ylabel='Density'>
Out[21]:
Text(0.5, 1.0, 'KDE of Humidity_Fallbrook')
Out[21]:
Text(0.5, 0, 'Humidity_Fallbrook')
Out[21]:
Text(0, 0.5, 'Density')
Out[21]:
<Axes: xlabel='Wind_Speed_Fallbrook', ylabel='Density'>
Out[21]:
<Axes: xlabel='Wind_Speed_Fallbrook', ylabel='Density'>
Out[21]:
Text(0.5, 1.0, 'KDE of Wind_Speed_Fallbrook')
Out[21]:
Text(0.5, 0, 'Wind_Speed_Fallbrook')
Out[21]:
Text(0, 0.5, 'Density')
Out[21]:
<Axes: xlabel='Visibility_Fallbrook', ylabel='Density'>
Out[21]:
<Axes: xlabel='Visibility_Fallbrook', ylabel='Density'>
Out[21]:
Text(0.5, 1.0, 'KDE of Visibility_Fallbrook')
Out[21]:
Text(0.5, 0, 'Visibility_Fallbrook')
Out[21]:
Text(0, 0.5, 'Density')
Out[21]:
<Axes: xlabel='Dew_point_temperature_Fallbrook', ylabel='Density'>
Out[21]:
<Axes: xlabel='Dew_point_temperature_Fallbrook', ylabel='Density'>
Out[21]:
Text(0.5, 1.0, 'KDE of Dew_point_temperature_Fallbrook')
Out[21]:
Text(0.5, 0, 'Dew_point_temperature_Fallbrook')
Out[21]:
Text(0, 0.5, 'Density')
No description has been provided for this image
In [22]:
# Pairplot for Fallbrook Weather Data
pairplot = sns.pairplot(input_data[weather_fallbrook], plot_kws={
                        'color': 'forestgreen'}, diag_kws={'color': 'forestgreen'})
pairplot.fig.suptitle(
    '\nPairwise Distribution of Fallbrook Weather Factors\n\n', fontsize=8, y=1.06)
pairplot.fig.set_size_inches(20, 18)
# Adjust the font size of the leftmost y-axis labels
for i, ax in enumerate(pairplot.axes[:, 0]):
    ax.set_ylabel(ax.get_ylabel(), fontsize=8)

# Adjust the font size of the bottom x-axis labels
for ax in pairplot.axes[-1, :]:
    ax.set_xlabel(ax.get_xlabel(), fontsize=8)
plt.show()
Out[22]:
Text(0.5, 1.06, '\nPairwise Distribution of Fallbrook Weather Factors\n\n')
Out[22]:
Text(67.8611111111111, 0.5, 'Temperature_Fallbrook')
Out[22]:
Text(57.3611111111111, 0.5, 'Sea_Level_Pressure_Fallbrook')
Out[22]:
Text(67.8611111111111, 0.5, 'Humidity_Fallbrook')
Out[22]:
Text(62.6111111111111, 0.5, 'Wind_Speed_Fallbrook')
Out[22]:
Text(67.7361111111111, 0.5, 'Visibility_Fallbrook')
Out[22]:
Text(64.6111111111111, 0.5, 'Dew_point_temperature_Fallbrook')
Out[22]:
Text(0.5, 52.11111111111096, 'Temperature_Fallbrook')
Out[22]:
Text(0.5, 52.11111111111096, 'Sea_Level_Pressure_Fallbrook')
Out[22]:
Text(0.5, 52.11111111111096, 'Humidity_Fallbrook')
Out[22]:
Text(0.5, 52.11111111111096, 'Wind_Speed_Fallbrook')
Out[22]:
Text(0.5, 52.11111111111096, 'Visibility_Fallbrook')
Out[22]:
Text(0.5, 52.11111111111096, 'Dew_point_temperature_Fallbrook')
No description has been provided for this image
In [23]:
# Descriptive Statistics for Uruapan Weather Data
with pd.option_context('float_format', '{:f}'.format):
    input_data[weather_uruapan].describe().T
Out[23]:
count mean std min 25% 50% 75% max
Temperature_Uruapan 216.000000 20.603093 1.415372 17.280303 19.741589 20.443585 21.600767 24.635443
Sea_Level_Pressure_Uruapan 216.000000 635.813458 0.572428 634.337121 635.451312 635.816259 636.230783 637.113317
Humidity_Uruapan 216.000000 67.251374 13.404664 36.744063 57.362114 68.695882 79.500787 85.725191
Wind_Speed_Uruapan 216.000000 1.799516 0.314965 0.967662 1.561724 1.754706 2.009551 2.506596
Visibility_Uruapan 216.000000 13.408285 2.519041 7.799501 11.546415 13.192788 14.922268 20.525341
Dew_point_temperature_Uruapan 216.000000 13.461364 3.381558 5.142480 10.256261 13.792843 16.698894 17.846154
In [24]:
# Correlation Heatmap for Uruapan Weather Data
plt.figure(figsize=(10, 8))
sns.heatmap(input_data[weather_uruapan].corr(),
            annot=True, cmap='Greens', fmt='.2f', linewidths=0.5)
plt.title('\nCorrelation Heatmap of Uruapan Weather Factors\n', fontsize=14)
plt.show()
Out[24]:
<Figure size 1000x800 with 0 Axes>
Out[24]:
<Axes: >
Out[24]:
Text(0.5, 1.0, '\nCorrelation Heatmap of Uruapan Weather Factors\n')
No description has been provided for this image
In [25]:
# KDE Plots for Uruapan Weather Data
fig, axes = plt.subplots(2, 3, figsize=(20, 10))
for i, col in enumerate(weather_uruapan):
    row, col_idx = divmod(i, 3)
    sns.kdeplot(data=input_data, x=col,
                ax=axes[row, col_idx], color='forestgreen', fill=True)
    sns.rugplot(input_data[col], ax=axes[row, col_idx],
                color='seagreen', linewidth=1, height=0.04)
    axes[row, col_idx].set_title(f'KDE of {col}', fontsize=10)
    axes[row, col_idx].tick_params(axis='both', which='major', labelsize=10)
    axes[row, col_idx].set_xlabel(col, fontsize=10)
    axes[row, col_idx].set_ylabel('Density', fontsize=10)
plt.subplots_adjust(hspace=0.4, wspace=0.4)
plt.show()
Out[25]:
<Axes: xlabel='Temperature_Uruapan', ylabel='Density'>
Out[25]:
<Axes: xlabel='Temperature_Uruapan', ylabel='Density'>
Out[25]:
Text(0.5, 1.0, 'KDE of Temperature_Uruapan')
Out[25]:
Text(0.5, 0, 'Temperature_Uruapan')
Out[25]:
Text(0, 0.5, 'Density')
Out[25]:
<Axes: xlabel='Sea_Level_Pressure_Uruapan', ylabel='Density'>
Out[25]:
<Axes: xlabel='Sea_Level_Pressure_Uruapan', ylabel='Density'>
Out[25]:
Text(0.5, 1.0, 'KDE of Sea_Level_Pressure_Uruapan')
Out[25]:
Text(0.5, 0, 'Sea_Level_Pressure_Uruapan')
Out[25]:
Text(0, 0.5, 'Density')
Out[25]:
<Axes: xlabel='Humidity_Uruapan', ylabel='Density'>
Out[25]:
<Axes: xlabel='Humidity_Uruapan', ylabel='Density'>
Out[25]:
Text(0.5, 1.0, 'KDE of Humidity_Uruapan')
Out[25]:
Text(0.5, 0, 'Humidity_Uruapan')
Out[25]:
Text(0, 0.5, 'Density')
Out[25]:
<Axes: xlabel='Wind_Speed_Uruapan', ylabel='Density'>
Out[25]:
<Axes: xlabel='Wind_Speed_Uruapan', ylabel='Density'>
Out[25]:
Text(0.5, 1.0, 'KDE of Wind_Speed_Uruapan')
Out[25]:
Text(0.5, 0, 'Wind_Speed_Uruapan')
Out[25]:
Text(0, 0.5, 'Density')
Out[25]:
<Axes: xlabel='Visibility_Uruapan', ylabel='Density'>
Out[25]:
<Axes: xlabel='Visibility_Uruapan', ylabel='Density'>
Out[25]:
Text(0.5, 1.0, 'KDE of Visibility_Uruapan')
Out[25]:
Text(0.5, 0, 'Visibility_Uruapan')
Out[25]:
Text(0, 0.5, 'Density')
Out[25]:
<Axes: xlabel='Dew_point_temperature_Uruapan', ylabel='Density'>
Out[25]:
<Axes: xlabel='Dew_point_temperature_Uruapan', ylabel='Density'>
Out[25]:
Text(0.5, 1.0, 'KDE of Dew_point_temperature_Uruapan')
Out[25]:
Text(0.5, 0, 'Dew_point_temperature_Uruapan')
Out[25]:
Text(0, 0.5, 'Density')
No description has been provided for this image
In [26]:
# Pairplot for Uruapan Weather Data
pairplot = sns.pairplot(input_data[weather_uruapan], plot_kws={
                        'color': 'forestgreen'}, diag_kws={'color': 'forestgreen'})
pairplot.fig.suptitle(
    '\nPairwise Distribution of Uruapan Weather Factors\n\n', fontsize=13, y=1.06)
pairplot.fig.set_size_inches(20, 18)
# Adjust the font size of the leftmost y-axis labels
for i, ax in enumerate(pairplot.axes[:, 0]):
    ax.set_ylabel(ax.get_ylabel(), fontsize=8)

# Adjust the font size of the bottom x-axis labels
for ax in pairplot.axes[-1, :]:
    ax.set_xlabel(ax.get_xlabel(), fontsize=8)
plt.show()
Out[26]:
Text(0.5, 1.06, '\nPairwise Distribution of Uruapan Weather Factors\n\n')
Out[26]:
Text(67.7361111111111, 0.5, 'Temperature_Uruapan')
Out[26]:
Text(57.3611111111111, 0.5, 'Sea_Level_Pressure_Uruapan')
Out[26]:
Text(67.9861111111111, 0.5, 'Humidity_Uruapan')
Out[26]:
Text(62.6111111111111, 0.5, 'Wind_Speed_Uruapan')
Out[26]:
Text(51.9861111111111, 0.5, 'Visibility_Uruapan')
Out[26]:
Text(51.9861111111111, 0.5, 'Dew_point_temperature_Uruapan')
Out[26]:
Text(0.5, 52.11111111111096, 'Temperature_Uruapan')
Out[26]:
Text(0.5, 52.11111111111096, 'Sea_Level_Pressure_Uruapan')
Out[26]:
Text(0.5, 52.11111111111096, 'Humidity_Uruapan')
Out[26]:
Text(0.5, 52.11111111111096, 'Wind_Speed_Uruapan')
Out[26]:
Text(0.5, 52.11111111111096, 'Visibility_Uruapan')
Out[26]:
Text(0.5, 52.11111111111096, 'Dew_point_temperature_Uruapan')
No description has been provided for this image

Energy Data in California¶

In [27]:
# Descriptive Statistics for CA Energy Data
with pd.option_context('float_format', '{:f}'.format):
    input_data[ca_energy].describe().T
Out[27]:
count mean std min 25% 50% 75% max
California_Gas_Price 216.000000 3.757833 0.894529 2.477000 3.095750 3.555500 4.331250 6.294000
California_NG_Price 216.000000 11.070895 3.149315 0.000000 9.085833 9.953333 12.345833 22.953333
California_Electricity_Price 216.000000 18.180000 3.393409 12.600000 15.497500 17.310000 20.007500 27.740000
In [28]:
# Correlation Heatmap for CA Energy Data
plt.figure(figsize=(10, 8))
sns.heatmap(input_data[ca_energy].corr(), annot=True,
            cmap='Reds', fmt='.2f', linewidths=0.5)
plt.title('\nCorrelation Heatmap of California Energy Factors\n', fontsize=14)
plt.show()
Out[28]:
<Figure size 1000x800 with 0 Axes>
Out[28]:
<Axes: >
Out[28]:
Text(0.5, 1.0, '\nCorrelation Heatmap of California Energy Factors\n')
No description has been provided for this image
In [29]:
# KDE Plots for CA Energy Data
fig, axes = plt.subplots(1, 3, figsize=(20, 5))
for i, col in enumerate(ca_energy):
    sns.kdeplot(data=input_data, x=col,
                ax=axes[i], color='firebrick', fill=True)
    sns.rugplot(input_data[col], ax=axes[i],
                color='darkred', linewidth=1, height=0.04)
    axes[i].set_title(f'KDE of {col}', fontsize=10)
    axes[i].tick_params(axis='both', which='major', labelsize=10)
    axes[i].set_xlabel(col, fontsize=10)
    axes[i].set_ylabel('Density', fontsize=10)
plt.subplots_adjust(hspace=0.4, wspace=0.4)
plt.show()
Out[29]:
<Axes: xlabel='California_Gas_Price', ylabel='Density'>
Out[29]:
<Axes: xlabel='California_Gas_Price', ylabel='Density'>
Out[29]:
Text(0.5, 1.0, 'KDE of California_Gas_Price')
Out[29]:
Text(0.5, 0, 'California_Gas_Price')
Out[29]:
Text(0, 0.5, 'Density')
Out[29]:
<Axes: xlabel='California_NG_Price', ylabel='Density'>
Out[29]:
<Axes: xlabel='California_NG_Price', ylabel='Density'>
Out[29]:
Text(0.5, 1.0, 'KDE of California_NG_Price')
Out[29]:
Text(0.5, 0, 'California_NG_Price')
Out[29]:
Text(0, 0.5, 'Density')
Out[29]:
<Axes: xlabel='California_Electricity_Price', ylabel='Density'>
Out[29]:
<Axes: xlabel='California_Electricity_Price', ylabel='Density'>
Out[29]:
Text(0.5, 1.0, 'KDE of California_Electricity_Price')
Out[29]:
Text(0.5, 0, 'California_Electricity_Price')
Out[29]:
Text(0, 0.5, 'Density')
No description has been provided for this image
In [30]:
# Pairplot for CA Energy Data
pairplot = sns.pairplot(input_data[ca_energy], plot_kws={
                        'color': 'firebrick'}, diag_kws={'color': 'firebrick'})
pairplot.fig.suptitle(
    '\nPairwise Distribution of California Energy Factors\n\n', fontsize=13, y=1.06)
pairplot.fig.set_size_inches(20, 18)
# Adjust the font size of the leftmost y-axis labels
for i, ax in enumerate(pairplot.axes[:, 0]):
    ax.set_ylabel(ax.get_ylabel(), fontsize=8)

# Adjust the font size of the bottom x-axis labels
for ax in pairplot.axes[-1, :]:
    ax.set_xlabel(ax.get_xlabel(), fontsize=8)
plt.show()
Out[30]:
Text(0.5, 1.06, '\nPairwise Distribution of California Energy Factors\n\n')
Out[30]:
Text(60.361111111111114, 0.5, 'California_Gas_Price')
Out[30]:
Text(49.861111111111114, 0.5, 'California_NG_Price')
Out[30]:
Text(49.861111111111114, 0.5, 'California_Electricity_Price')
Out[30]:
Text(0.5, 44.61111111111103, 'California_Gas_Price')
Out[30]:
Text(0.5, 44.61111111111103, 'California_NG_Price')
Out[30]:
Text(0.5, 44.61111111111103, 'California_Electricity_Price')
No description has been provided for this image

Summary of Data Review¶

The analysis of 216 monthly avocado price points spanning from January 2015 to December 2023, encompassing both organic and conventional avocados, yielded the following insights:

  1. Data Completeness: No null values were found across all fields within the dataset.

  2. Price Stationarity:

    • Visual inspection of price point distribution plots suggests stationarity.
    • Augmented Dickey-Fuller (ADF) Test results with a p-value of approximately 0.028, below the chosen significance level of 0.05, reject the null hypothesis, indicating that the price data is indeed stationary.

  3. Plantation Data Evaluation:

    • Evaluation plots of plantation data from Fallbrook and Uruapan, assessed using Kernel Density Estimation (KDE) plots with automatic bandwidth selection, indicate normally distributed attributes without any outliers.

  4. Energy Data Evaluation:

    • Similar KDE evaluation of energy data in California reveals normally distributed attributes with no identified outliers.

  5. Economic Data Correlation:

    • Analysis of economic data using an attribute correlation heatmap reveals significant correlations between certain variables.
    • Notably, Unemployment_Level correlates highly with Unemployment_Rate; Average_Hourly_Earnings_of_All_Employees correlates with Personal_Consumption_Expenditures; and Employed_Persons_in_California correlates with Labor_Force_Participation_Rate_for_California.
    • Consequently, Unemployment_Level, Average_Hourly_Earnings_of_All_Employees, and Employed_Persons_in_California are excluded from the model development process.

  6. Economic Factors Manipulation:

    • Economic factors are adjusted into leading indicators, implying that changes in economic factors may lag behind changes in avocado prices.
    • For example, a rise in unemployment may not immediately impact avocado prices within the same month but could affect the price changes two months later.
    • Considering this lag effect, each avocado price point incorporates economic factors not only from the month of avocado pricing but also from two months prior.

Model Development¶

Methodology and Model Development¶

To estimate avocado prices based on various input features, the linear regression model is commonly utilized. This model represents a linear combination of features and their respective coefficients. Advanced techniques in linear regression may involve mapping input attributes to higher-dimensional feature spaces and incorporating interaction terms to capture synergy effects. Additionally, local data fitting methods, such as locally weighted regression, can enhance model accuracy.

In the development of a linear regression model, selecting the most important features is crucial. Three commonly used feature selection techniques in linear regression are Forward Selection, Backward Elimination, and Recursive Feature Elimination. Below are descriptions of each technique:

Forward Selection:¶

  1. Begins with an empty set of selected features.
  2. Iteratively selects the best feature to add to the selected set based on improvements in model performance.
  3. Continues this process until the desired number of features is selected.

Backward Elimination:¶

  1. Starts with all features included in the selected features set.
  2. Iteratively removes the worst-performing feature based on degradation in model performance.
  3. Continues until the number of selected features reaches the minimum desired number.

Recursive Feature Elimination:¶

  1. Iterates through each remaining feature.
  2. Adds the feature to the selected features.
  3. Trains the model using the selected features.
  4. Evaluates the model performance using a chosen metric.
  5. If the model performance improves, updates the best score and best feature.
  6. Backtracks by removing the feature to explore other features.

For this project, linear regression with feature elimination is not considered due to the simplicity of the linear regression model. While linear regression offers good interpretability compared to other regression models, its simplicity may not effectively model the complex nonlinear relationships inherent in avocado prices. Instead, regression trees and random forest models will be developed using 80% of the input data for training. The remaining 20% of the data will be used to evaluate the performance of the regression tree and random forest models.

Part II: Model Development¶

In [31]:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib import rcParams
import seaborn as sns
from sklearn.model_selection import train_test_split, GridSearchCV, cross_val_score
from sklearn.ensemble import RandomForestRegressor
from sklearn.tree import DecisionTreeRegressor, plot_tree
from sklearn.metrics import r2_score
In [32]:
# Set plotting styles and configurations

# Set the plot style to 'ggplot' for consistent visual style
plt.style.use('ggplot')

# Configure matplotlib parameters to remove right and top spines, and set figure size
rcParams['axes.spines.right'] = False
rcParams['axes.spines.top'] = False
rcParams['figure.figsize'] = [12, 9]

# Set font size for plot labels and titles
rcParams['font.size'] = 12

# Set tick label sizes for both x and y axes
plt.rc('xtick', labelsize=10)
plt.rc('ytick', labelsize=10)

# Define custom colors for seaborn plots
custom_colors = ['#74a09e', '#86c1b2', '#98e2c6',
                 '#f3c969', '#f2a553', '#d96548', '#c14953']
sns.set_palette(custom_colors)

# Configure inline figure format for high-resolution displays
%config InlineBackend.figure_format = 'retina'

# Disable Jedi for auto-completion to potentially improve performance in large notebooks
%config Completer.use_jedi = False
In [33]:
# Load data and preprocess

# Set random seed for reproducibility
np.random.seed(42)

# Load data from Excel file into DataFrame
Input_Data = pd.read_excel('Data_project.xls')


# Columns to remove from the dataset
Remove_Col = ['Unemployment_Level', 'Average_Hourly_Earnings_of_All_Employees',
              'Employed_Persons_in_California', 'Unemployment_Level_Lead2',
              'Average_Hourly_Earnings_of_All_Employees_Lead2', 'Employed_Persons_in_California_Lead2']

# Filter columns to retain only those not in Remove_Col
filtered_columns = [col for col in Input_Data.columns if col not in Remove_Col]
filtered_input = Input_Data[filtered_columns]

# Split the filtered data into features (X) and labels (y)
features, labels = filtered_input.iloc[:, 1:31], filtered_input.iloc[:, 32]

# Split the data into training and testing sets using a 80%-20% split ratio
Xtrain, Xtest, ytrain, ytest = train_test_split(
    features, labels, test_size=0.2, shuffle=True, random_state=6)
In [34]:
Input_Data
Out[34]:
Year_Month Year Month Is_Organic Unemployment_Level Unemployment_Level_Lead2 Unemployment_Rate Unemployment_Rate_Lead2 Median_Consumer_Price_Index Median_Consumer_Price_Index_Lead2 Personal_Consumption_Expenditures Personal_Consumption_Expenditures_Lead2 Number_Unemployed_for_27_Weeks_&_over Number_Unemployed_for_27_Weeks_&_over_Lead2 Average_Hourly_Earnings_of_All_Employees Average_Hourly_Earnings_of_All_Employees_Lead2 Federal_Funds_Effective_Rate Federal_Funds_Effective_Rate_Lead2 Employed_Persons_in_California Employed_Persons_in_California_Lead2 Labor_Force_Participation_Rate_for_California Labor_Force_Participation_Rate_for_California_Lead2 California_Gas_Price California_NG_Price California_Electricity_Price Temperature_Uruapan Sea_Level_Pressure_Uruapan Humidity_Uruapan Wind_Speed_Uruapan Visibility_Uruapan Dew_point_temperature_Uruapan Temperature_Fallbrook Sea_Level_Pressure_Fallbrook Humidity_Fallbrook Wind_Speed_Fallbrook Visibility_Fallbrook Dew_point_temperature_Fallbrook Avocado_Volume Avocado_Price
0 201501 2015 1 0 8885 9090 5.7 5.8 1.947530 2.256311 12066.7 12083.9 2774 2828 24.75 24.66 0.11 0.09 17513360 17451977 62.3 62.4 2.596 9.436667 14.55 19.061947 635.875221 65.601770 2.000000 17.190400 11.823009 14.600514 745.208895 54.552699 1.538817 14.875681 3.757841 5.575767e+06 0.982500
1 201501 2015 1 1 8885 9090 5.7 5.8 1.947530 2.256311 12066.7 12083.9 2774 2828 24.75 24.66 0.11 0.09 17513360 17451977 62.3 62.4 2.596 9.436667 14.55 19.061947 635.875221 65.601770 2.000000 17.190400 11.823009 14.600514 745.208895 54.552699 1.538817 14.875681 3.757841 1.543415e+05 1.220000
2 201502 2015 2 0 8599 8717 5.5 5.6 1.954495 2.383394 12116.6 12096.1 2658 2799 24.79 24.62 0.11 0.12 17539526 17484592 62.3 62.4 2.756 8.960000 14.30 17.801887 635.096226 69.198113 1.320755 19.773585 11.424528 15.616625 743.596898 61.901985 1.638337 14.462779 6.569479 6.638805e+06 0.920000
3 201502 2015 2 1 8599 8717 5.5 5.6 1.954495 2.383394 12116.6 12096.1 2658 2799 24.79 24.62 0.11 0.12 17539526 17484592 62.3 62.4 2.756 8.960000 14.30 17.801887 635.096226 69.198113 1.320755 19.773585 11.424528 15.616625 743.596898 61.901985 1.638337 14.462779 6.569479 1.454359e+05 1.347500
4 201503 2015 3 0 8515 8885 5.4 5.7 2.433336 1.947530 12176.1 12066.7 2542 2774 24.86 24.75 0.11 0.11 17566611 17513360 62.3 62.3 3.388 8.960000 14.22 19.078431 635.006000 68.745098 2.385621 15.735948 12.333333 17.691583 743.619033 56.874372 1.791457 14.905528 6.533291 5.832235e+06 1.004000
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
211 202310 2023 10 1 6443 6340 3.8 3.8 3.497958 4.358972 18826.8 18651.6 1291 1326 34.10 33.91 5.33 5.33 18345357 18390468 62.1 62.1 5.546 13.330000 24.33 20.538084 634.921376 83.375921 1.454545 12.248649 17.486486 19.208597 741.018597 68.074208 1.508152 15.038552 11.113575 2.639227e+05 1.720990
212 202311 2023 11 0 6262 6347 3.7 3.8 5.122615 5.217921 18903.0 18791.5 1220 1303 34.23 34.01 5.33 5.33 18331874 18358415 62.0 62.0 4.935 15.693333 24.37 20.901015 635.970305 74.746193 1.555838 13.278173 15.959391 16.811682 743.497710 48.300935 2.076382 15.545582 2.702804 4.928270e+06 1.248331
213 202311 2023 11 1 6262 6347 3.7 3.8 5.122615 5.217921 18903.0 18791.5 1220 1303 34.23 34.01 5.33 5.33 18331874 18358415 62.0 62.0 4.935 15.693333 24.37 20.901015 635.970305 74.746193 1.555838 13.278173 15.959391 16.811682 743.497710 48.300935 2.076382 15.545582 2.702804 2.694976e+05 1.728536
214 202312 2023 12 0 6268 6443 3.7 3.8 4.160125 3.497958 19013.7 18826.8 1245 1291 34.34 34.10 5.33 5.33 18351873 18345357 62.1 62.1 4.558 15.793333 24.16 18.745636 635.424938 70.476309 1.284289 13.969077 12.872818 14.373195 744.320442 63.308664 1.622162 15.230144 5.408394 5.845933e+06 1.066007
215 202312 2023 12 1 6268 6443 3.7 3.8 4.160125 3.497958 19013.7 18826.8 1245 1291 34.34 34.10 5.33 5.33 18351873 18345357 62.1 62.1 4.558 15.793333 24.16 18.745636 635.424938 70.476309 1.284289 13.969077 12.872818 14.373195 744.320442 63.308664 1.622162 15.230144 5.408394 2.909444e+05 1.663419

216 rows × 39 columns

Classification And Regression Tree¶

In [35]:
# Decision Tree parameter tuning with cross-validation

# Define a list of minimum samples per leaf to evaluate
min_sample_leaf = [i * 3 + 3 for i in range(10)]

# Lists to store mean R2 scores and their standard deviations
CART_r2 = []
std_CART_r2 = []

# Iterate over each value of min_samples_leaf
for num_sample in min_sample_leaf:
    # Initialize DecisionTreeRegressor with specified parameters
    DT_CV = DecisionTreeRegressor(random_state=42, min_samples_leaf=num_sample)

    # Perform cross-validation with 5 folds, using R2 as the scoring metric
    scores = cross_val_score(DT_CV, Xtrain, ytrain, cv=5, scoring='r2')

    # Append mean R2 score to CART_r2 list
    CART_r2.append(np.mean(scores))

    # Append standard deviation of R2 scores to std_CART_r2 list
    std_CART_r2.append(np.std(scores))

# Calculate upper and lower bounds of R2 scores for plotting error bars
R2_upper = np.array(CART_r2) + np.array(std_CART_r2)
R2_lower = np.array(CART_r2) - np.array(std_CART_r2)
In [36]:
# Plotting CV results

# Set figure size
plt.figure(figsize=(16, 8))

# Plot mean R2 scores against min_samples_leaf
plt.plot(min_sample_leaf, CART_r2, marker='o', label='r2', color='darkblue')

# Plot upper and lower bounds for standard deviation of R2 scores
plt.plot(min_sample_leaf, R2_upper, linestyle='--',
         color='black', label='Upper/Lower Std')
plt.plot(min_sample_leaf, R2_lower, linestyle='--', color='black')

# Label x-axis and y-axis
plt.xlabel('Num of min_samples_leaf')
plt.ylabel('r2')

# Add text annotations for each point on the plot
for x, y in zip(min_sample_leaf, CART_r2):
    plt.text(x - 0.8, y - 0.03, f'({x}, {y:.3f})',
             ha='left', fontsize=9, color='darkblue')

# Set y-axis limits
plt.ylim(0.3, 1.0)

# Set plot title
plt.title('Result of 5-fold CV')

# Display legend in upper right corner
plt.legend(loc='upper right')

# Show the plot
plt.show()
Out[36]:
<Figure size 1600x800 with 0 Axes>
Out[36]:
[<matplotlib.lines.Line2D at 0x7af1ace4b550>]
Out[36]:
[<matplotlib.lines.Line2D at 0x7af1ace4b820>]
Out[36]:
[<matplotlib.lines.Line2D at 0x7af1ace4bac0>]
Out[36]:
Text(0.5, 0, 'Num of min_samples_leaf')
Out[36]:
Text(0, 0.5, 'r2')
Out[36]:
Text(2.2, 0.5419641857669162, '(3, 0.572)')
Out[36]:
Text(5.2, 0.5951415027286562, '(6, 0.625)')
Out[36]:
Text(8.2, 0.5744076206926568, '(9, 0.604)')
Out[36]:
Text(11.2, 0.6041838217547283, '(12, 0.634)')
Out[36]:
Text(14.2, 0.62274187411659, '(15, 0.653)')
Out[36]:
Text(17.2, 0.5975570493749578, '(18, 0.628)')
Out[36]:
Text(20.2, 0.5803802210871718, '(21, 0.610)')
Out[36]:
Text(23.2, 0.5628477522088877, '(24, 0.593)')
Out[36]:
Text(26.2, 0.5509404413896395, '(27, 0.581)')
Out[36]:
Text(29.2, 0.5582629796903819, '(30, 0.588)')
Out[36]:
(0.3, 1.0)
Out[36]:
Text(0.5, 1.0, 'Result of 5-fold CV')
Out[36]:
<matplotlib.legend.Legend at 0x7af1ace4b6a0>
No description has been provided for this image
In [37]:
# Visualize the Decision Tree

# Initialize DecisionTreeRegressor with specified parameters
clf_CART = DecisionTreeRegressor(random_state=42, min_samples_leaf=15)

# Fit the Decision Tree model on training data
clf_CART.fit(Xtrain, ytrain)

# Set the figure size for the plot
plt.figure(figsize=(20, 10))

# Plot the Decision Tree
plot_tree(clf_CART, filled=False, feature_names=features.columns, fontsize=8)

# Display the plot
plt.show()
Out[37]:
DecisionTreeRegressor(min_samples_leaf=15, random_state=42)
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
DecisionTreeRegressor(min_samples_leaf=15, random_state=42)
Out[37]:
<Figure size 2000x1000 with 0 Axes>
Out[37]:
[Text(0.375, 0.9166666666666666, 'Is_Organic <= 0.5\nsquared_error = 0.13\nsamples = 172\nvalue = 1.503'),
 Text(0.16666666666666666, 0.75, 'Personal_Consumption_Expenditures_Lead2 <= 13072.9\nsquared_error = 0.042\nsamples = 89\nvalue = 1.234'),
 Text(0.08333333333333333, 0.5833333333333334, 'squared_error = 0.027\nsamples = 23\nvalue = 1.027'),
 Text(0.25, 0.5833333333333334, 'Dew_point_temperature_Fallbrook <= 13.664\nsquared_error = 0.026\nsamples = 66\nvalue = 1.306'),
 Text(0.16666666666666666, 0.4166666666666667, 'Federal_Funds_Effective_Rate <= 1.155\nsquared_error = 0.019\nsamples = 48\nvalue = 1.257'),
 Text(0.08333333333333333, 0.25, 'squared_error = 0.015\nsamples = 18\nvalue = 1.36'),
 Text(0.25, 0.25, 'Number_Unemployed_for_27_Weeks_&_over_Lead2 <= 1289.0\nsquared_error = 0.011\nsamples = 30\nvalue = 1.196'),
 Text(0.16666666666666666, 0.08333333333333333, 'squared_error = 0.009\nsamples = 15\nvalue = 1.237'),
 Text(0.3333333333333333, 0.08333333333333333, 'squared_error = 0.009\nsamples = 15\nvalue = 1.154'),
 Text(0.3333333333333333, 0.4166666666666667, 'squared_error = 0.024\nsamples = 18\nvalue = 1.435'),
 Text(0.5833333333333334, 0.75, 'Personal_Consumption_Expenditures_Lead2 <= 12743.95\nsquared_error = 0.064\nsamples = 83\nvalue = 1.792'),
 Text(0.5, 0.5833333333333334, 'squared_error = 0.037\nsamples = 16\nvalue = 1.49'),
 Text(0.6666666666666666, 0.5833333333333334, 'Temperature_Fallbrook <= 16.969\nsquared_error = 0.043\nsamples = 67\nvalue = 1.864'),
 Text(0.5, 0.4166666666666667, 'Temperature_Fallbrook <= 14.505\nsquared_error = 0.028\nsamples = 37\nvalue = 1.761'),
 Text(0.4166666666666667, 0.25, 'squared_error = 0.026\nsamples = 22\nvalue = 1.714'),
 Text(0.5833333333333334, 0.25, 'squared_error = 0.023\nsamples = 15\nvalue = 1.829'),
 Text(0.8333333333333334, 0.4166666666666667, 'California_NG_Price <= 9.898\nsquared_error = 0.033\nsamples = 30\nvalue = 1.991'),
 Text(0.75, 0.25, 'squared_error = 0.029\nsamples = 15\nvalue = 2.073'),
 Text(0.9166666666666666, 0.25, 'squared_error = 0.023\nsamples = 15\nvalue = 1.908')]
No description has been provided for this image
In [38]:
# Evaluate Decision Tree performance

# Predict on training and testing data
y_pred_train = clf_CART.predict(Xtrain)
y_pred_test = clf_CART.predict(Xtest)

# Calculate R2 scores for training and testing data
r2_train = r2_score(ytrain, y_pred_train)
r2_test = r2_score(ytest, y_pred_test)

# Print the R2 scores
print(f"R2 score on training data: {r2_train:.3f}")
print(f"R2 score on testing data: {r2_test:.3f}")

R2 score on training data: 0.827
R2 score on testing data: 0.589
In [39]:
# Calculate feature importances from the Decision Tree model
feature_importances = clf_CART.feature_importances_

# Create a DataFrame to store feature names and their importances
feature_importance_df = pd.DataFrame({
    'Feature': Xtrain.columns,
    'Importance': feature_importances
})

# Sort the DataFrame by importance in descending order
feature_importance_df = feature_importance_df.sort_values(
    by='Importance', ascending=False)

# Select the top 10 most important features
feature_importance_df = feature_importance_df.head(10)

# Display the DataFrame with the top 10 important features
feature_importance_df
Out[39]:
Feature Importance
2 Is_Organic 0.723765
8 Personal_Consumption_Expenditures_Lead2 0.169634
24 Temperature_Fallbrook 0.053859
29 Dew_point_temperature_Fallbrook 0.022358
11 Federal_Funds_Effective_Rate 0.016434
16 California_NG_Price 0.011114
10 Number_Unemployed_for_27_Weeks_&_ove... 0.002836
27 Wind_Speed_Fallbrook 0.000000
26 Humidity_Fallbrook 0.000000
25 Sea_Level_Pressure_Fallbrook 0.000000
In [40]:
# Plotting the feature importances
plt.figure(figsize=(14, 6))

# Create horizontal bars for each feature, using importance scores as bar lengths
bars = plt.barh(feature_importance_df['Feature'],
                feature_importance_df['Importance'], color='seagreen')

# Set labels and title
plt.xlabel('Importance Score')
plt.ylabel('')
plt.title('\nRegression Tree - Feature Importances (Top 10)')

# Add text annotations showing the numerical value of each importance score next to its corresponding bar
for bar, importance in zip(bars, feature_importance_df['Importance']):
    plt.text(bar.get_width() + 0.01, bar.get_y() + bar.get_height()/2, f'{importance:.3f}',
             va='center', ha='left', fontsize=11)

# Set limits and invert y-axis for better visualization
plt.xlim(0, 1)
plt.gca().invert_yaxis()

# Display the plot
plt.show()
Out[40]:
<Figure size 1400x600 with 0 Axes>
Out[40]:
Text(0.5, 0, 'Importance Score')
Out[40]:
Text(0, 0.5, '')
Out[40]:
Text(0.5, 1.0, '\nRegression Tree - Feature Importances (Top 10)')
Out[40]:
Text(0.7337654938220523, 0.0, '0.724')
Out[40]:
Text(0.17963381251014426, 1.0, '0.170')
Out[40]:
Text(0.06385899591104413, 2.0, '0.054')
Out[40]:
Text(0.032357560687732774, 3.0, '0.022')
Out[40]:
Text(0.0264338995490829, 4.0, '0.016')
Out[40]:
Text(0.02111378930348659, 5.0, '0.011')
Out[40]:
Text(0.012836448216457136, 6.0, '0.003')
Out[40]:
Text(0.01, 7.0, '0.000')
Out[40]:
Text(0.01, 8.0, '0.000')
Out[40]:
Text(0.01, 9.0, '0.000')
Out[40]:
(0.0, 1.0)
No description has been provided for this image

Random Forest¶

In [41]:
# Define lists of values for n_estimators and min_samples_leaf
# Generates values: [3, 6, 9, 12, 15, 18, 21, 24, 27, 30]
num_sample = [i * 3 + 3 for i in range(10)]
# Generates values: [40, 60, 80, 100, 120, 140, 160, 180, 200, 220]
num_tree = [i * 20 + 40 for i in range(10)]

# Define the parameter grid for Random Forest tuning
param_grid = {
    'n_estimators': num_tree,
    'min_samples_leaf': num_sample
}

# Initialize the Random Forest regressor
rf_model = RandomForestRegressor(random_state=42)

# Perform grid search cross-validation to find the best parameters
grid_search = GridSearchCV(
    estimator=rf_model, param_grid=param_grid, cv=5, scoring='r2', n_jobs=-1)
grid_search.fit(Xtrain, ytrain)

# Get the best parameters found by the grid search
best_params = grid_search.best_params_
print(best_params)

# Convert grid search CV results into a DataFrame
cv_results_df = pd.DataFrame(grid_search.cv_results_)

cv_results_df
Out[41]:
GridSearchCV(cv=5, estimator=RandomForestRegressor(random_state=42), n_jobs=-1,
             param_grid={'min_samples_leaf': [3, 6, 9, 12, 15, 18, 21, 24, 27,
                                              30],
                         'n_estimators': [40, 60, 80, 100, 120, 140, 160, 180,
                                          200, 220]},
             scoring='r2')
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GridSearchCV(cv=5, estimator=RandomForestRegressor(random_state=42), n_jobs=-1,
             param_grid={'min_samples_leaf': [3, 6, 9, 12, 15, 18, 21, 24, 27,
                                              30],
                         'n_estimators': [40, 60, 80, 100, 120, 140, 160, 180,
                                          200, 220]},
             scoring='r2')
RandomForestRegressor(random_state=42)
RandomForestRegressor(random_state=42)
{'min_samples_leaf': 3, 'n_estimators': 60}
Out[41]:
mean_fit_time std_fit_time mean_score_time std_score_time param_min_samples_leaf param_n_estimators params split0_test_score split1_test_score split2_test_score split3_test_score split4_test_score mean_test_score std_test_score rank_test_score
0 0.138444 0.001909 0.005966 0.000355 3 40 {'min_samples_leaf': 3, 'n_estimator... 0.783895 0.768727 0.841186 0.749061 0.779108 0.784395 0.030814 4
1 0.212894 0.013818 0.007717 0.000883 3 60 {'min_samples_leaf': 3, 'n_estimator... 0.792452 0.766091 0.839555 0.753848 0.778245 0.786038 0.029665 1
2 0.277188 0.011394 0.008253 0.000387 3 80 {'min_samples_leaf': 3, 'n_estimator... 0.798336 0.766719 0.829675 0.754325 0.771234 0.784058 0.026959 5
3 0.342243 0.011323 0.012151 0.005294 3 100 {'min_samples_leaf': 3, 'n_estimator... 0.799995 0.764629 0.828543 0.753067 0.776010 0.784449 0.026962 3
4 0.399282 0.001221 0.010707 0.000909 3 120 {'min_samples_leaf': 3, 'n_estimator... 0.803332 0.765748 0.829903 0.750270 0.774298 0.784710 0.028437 2
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
95 0.632766 0.020513 0.019193 0.005723 30 140 {'min_samples_leaf': 30, 'n_estimato... 0.598694 0.598064 0.530462 0.607146 0.550422 0.576958 0.030644 92
96 0.493477 0.135966 0.016462 0.005966 30 160 {'min_samples_leaf': 30, 'n_estimato... 0.599455 0.597967 0.529536 0.607649 0.550328 0.576987 0.031136 90
97 0.412797 0.009213 0.013629 0.000560 30 180 {'min_samples_leaf': 30, 'n_estimato... 0.598365 0.598452 0.528730 0.608180 0.550303 0.576806 0.031405 95
98 0.454056 0.013071 0.014602 0.000716 30 200 {'min_samples_leaf': 30, 'n_estimato... 0.599055 0.598213 0.528509 0.608461 0.550340 0.576916 0.031586 93
99 0.460707 0.056915 0.018209 0.008494 30 220 {'min_samples_leaf': 30, 'n_estimato... 0.599012 0.598459 0.528422 0.608457 0.550437 0.576958 0.031623 91

100 rows × 15 columns

In [42]:
# Pivot the DataFrame to create a matrix for heatmap visualization
matrix_df = cv_results_df.pivot(
    index='param_min_samples_leaf', columns='param_n_estimators', values='mean_test_score')

# Plotting the heatmap
plt.figure(figsize=(13, 8))
sns.heatmap(matrix_df, annot=True, fmt='.4f', cmap='PiYG',
            cbar=True, linewidths=0.5, annot_kws={'fontsize': 11})
plt.title('r2 Score Matrix')
plt.xlabel('n_estimators')
plt.ylabel('min_samples_leaf')
plt.show()
Out[42]:
<Figure size 1300x800 with 0 Axes>
Out[42]:
<Axes: xlabel='param_n_estimators', ylabel='param_min_samples_leaf'>
Out[42]:
Text(0.5, 1.0, 'r2 Score Matrix')
Out[42]:
Text(0.5, 58.7222222222222, 'n_estimators')
Out[42]:
Text(133.22222222222223, 0.5, 'min_samples_leaf')
No description has been provided for this image
In [43]:
# Train Random Forest with best parameters obtained from GridSearchCV
rf_model_organic = RandomForestRegressor(
    random_state=42, min_samples_leaf=3, n_estimators=60)
rf_model_organic.fit(Xtrain, ytrain)

# Evaluate Random Forest performance on training data
y_pred_train = rf_model_organic.predict(Xtrain)
r2_train = r2_score(ytrain, y_pred_train)
print(f"R2 score on training data: {r2_train:.3f}")

# Evaluate Random Forest performance on testing data
y_pred_test = rf_model_organic.predict(Xtest)
r2_test = r2_score(ytest, y_pred_test)
print(f"R2 score on testing data: {r2_test:.3f}")
Out[43]:
RandomForestRegressor(min_samples_leaf=3, n_estimators=60, random_state=42)
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RandomForestRegressor(min_samples_leaf=3, n_estimators=60, random_state=42)
R2 score on training data: 0.947
R2 score on testing data: 0.798
In [44]:
# Calculate feature importances and their standard deviations
feature_importances = rf_model_organic.feature_importances_
std_importances = np.std(
    [tree.feature_importances_ for tree in rf_model_organic.estimators_], axis=0)

# Create a DataFrame to store feature importances and standard deviations
feature_importance_df = pd.DataFrame({
    'Feature': Xtrain.columns,
    'Importance': feature_importances,
    'Std': std_importances
})

# Sort the DataFrame by Importance in descending order and select the top 10 features
feature_importance_df = feature_importance_df.sort_values(
    by='Importance', ascending=False).head(10)
feature_importance_df
Out[44]:
Feature Importance Std
2 Is_Organic 0.615962 0.037595
8 Personal_Consumption_Expenditures_Lead2 0.092856 0.065031
24 Temperature_Fallbrook 0.036723 0.033703
17 California_Electricity_Price 0.035480 0.053240
7 Personal_Consumption_Expenditures 0.032084 0.043673
22 Visibility_Uruapan 0.017089 0.021050
29 Dew_point_temperature_Fallbrook 0.015214 0.022278
25 Sea_Level_Pressure_Fallbrook 0.014365 0.020864
15 California_Gas_Price 0.014084 0.019424
1 Month 0.009497 0.024624
In [45]:
# Plotting the top 10 feature importances with error bars representing standard deviations
plt.figure(figsize=(14, 6))
bars = plt.barh(feature_importance_df['Feature'], feature_importance_df['Importance'],
                xerr=feature_importance_df['Std'], color='seagreen')
plt.xlabel('Importance Score')
plt.ylabel('')
plt.title('Random Forest - Feature Importances (Top 10)')

# Adding text annotations for each bar showing the importance score
for bar, importance in zip(bars, feature_importance_df['Importance']):
    plt.text(bar.get_width() + 0.01, bar.get_y() + bar.get_height() / 2, f'{importance:.3f}',
             va='center', ha='left', fontsize=11)

plt.xlim(0, 1)  # Setting x-axis limit from 0 to 1
# Inverting y-axis to display the most important feature on top
plt.gca().invert_yaxis()
plt.show()  # Display the plot
Out[45]:
<Figure size 1400x600 with 0 Axes>
Out[45]:
Text(0.5, 0, 'Importance Score')
Out[45]:
Text(0, 0.5, '')
Out[45]:
Text(0.5, 1.0, 'Random Forest - Feature Importances (Top 10)')
Out[45]:
Text(0.62596167516308, 0.0, '0.616')
Out[45]:
Text(0.10285616137000084, 1.0, '0.093')
Out[45]:
Text(0.04672286004637596, 2.0, '0.037')
Out[45]:
Text(0.04547997856799104, 3.0, '0.035')
Out[45]:
Text(0.042083941691795815, 4.0, '0.032')
Out[45]:
Text(0.02708858774320544, 5.0, '0.017')
Out[45]:
Text(0.025214405504405513, 6.0, '0.015')
Out[45]:
Text(0.024364713078400345, 7.0, '0.014')
Out[45]:
Text(0.02408448245406839, 8.0, '0.014')
Out[45]:
Text(0.019496988264817425, 9.0, '0.009')
Out[45]:
(0.0, 1.0)
No description has been provided for this image

Conclusion¶

This project aimed to compare and evaluate the performance of two regression models—Regression Tree and Random Forest—for predicting avocado prices. Each model was rigorously assessed using a comprehensive dataset, with a focus on interpretability, generalizability, and feature importance.

Regression Tree Analysis

The Regression Tree model, while intuitive and capable of capturing complex relationships, demonstrated limitations in generalizing to unseen data. The model achieved a training $R^2$ score of 0.827, indicating a good fit to the training dataset. However, its testing $R^2$ score of 0.589 suggested a considerable drop in performance on new data, highlighting its susceptibility to overfitting.

Random Forest Analysis

In contrast, the Random Forest model addressed the overfitting issue by aggregating predictions from multiple decision trees. Tuned through grid search cross-validation, the optimal configuration of $\text{min_samples_leaf} = 3$ and $\text{n_estimators} = 60$ yielded robust results. The Random Forest achieved a high training $R^2$ score of 0.947 and a testing $R^2$ score of 0.798, showcasing superior generalizability and less sensitivity to overfitting compared to the Regression Tree.

Feature Importance Insights

Feature importance analysis revealed key drivers influencing avocado prices. Organic designation significantly impacted prices, aligning with consumer preferences for higher-priced organic produce. Changes in personal consumption expenditures influenced prices with a two-month lag, highlighting economic factors' delayed impact on avocado markets. Additionally, local weather conditions and electricity prices in California played minor yet discernible roles in price fluctuations.

Conclusion and Implications

In conclusion, while the Regression Tree provides transparency in decision-making, its limited generalizability compromises its utility for robust predictions on unseen data. The Random Forest model, leveraging ensemble learning, offers superior predictive performance and feature interpretability, making it suitable for practical applications where accuracy and resilience to overfitting are paramount.

This study's findings suggest that leveraging Random Forest models can enhance the accuracy of price predictions in agricultural markets, with implications for broader analyses of food price dynamics. Future research could expand this methodology to explore additional economic and environmental variables impacting food prices across regions.